There are three basic types of arguments- Persuasive, Defensive, and Offensive-out of which extended versions can be constructed by combining various elements from each. Although they have different goals, each type has two common requirements: a clearly stated position, or claim, and authoritative evidence that an audience will find acceptable.
Knowing which type of argument to write depends a great deal on how you assess your audience and what your instructor asks for in the assignment. Here is a brief overview of each type and some hints about what to look for in the assignment.
Note: Offensive and persuasive arguments are often combined and the distinction is not often made in the actual assignment.